Find the value of "K"
\(\frac{-2}{3} ( \frac{1}{2} + k) = \frac{-55}{39}\)
\(\frac{-2}{3}*\frac{1}{2} + \frac{-2}{3}*k = \frac{-55}{39}\)
\(\frac{-2}{6} + \frac{-2k}{3} = \frac{-55}{39}\)
least common multiple (6,3,39) = 78
\(\frac{-26}{\diagup\!\!\!\!\!78} + \frac{-52k}{\diagup\!\!\!\!\!78} = \frac{-110}{\diagup\!\!\!\!\!78}\)
\(- 26 - 52k = - 110\)
\(- 52k = - 110 + 26\)
\(- 52k = - 84\:simplify\:by\:*(-1)\)
\(52k = 84\)
\(k = \frac{84}{52}\: \frac{\div4}{\div4} \to \boxed{\boxed{k = \frac{21}{13} }}\end{array}}\qquad\quad\checkmark\)
